Polarization, magnetisation, and other geometrical properties of the electronic ground state
Abstract
Some intensive observables in condensed matter (crystalline and noncrys- talline) have a geometrical or even topological nature. The term geometrical" does not refer to the geometry of the ordinary coordinate space; it refers in- stead to the geometry of the electronic ground state in some abstract parameter space. This proposal addresses the rst-principle theory of such observables of materials, and the implementation of algorithms to compute them. The archetype in this class of observables is the macroscopic electric po- larization of solids, whose geometricaal theory dates since 1992 onwards; rst- principle calculations are now routinely performed, providing understanding and predictions for a large class of ferroelectric and piezoelectric materials. Several other geometrical observables have been discovered afterwards, hav- ing very different experimental meanings, yet showing a common formal struc- ture from a theoretical viewpoint. It became also clear over the years that the geometrical observables come in two very different classes. The observables of class (i) only make sense for insulators, and are de ned modulo 2 (in dimen- sionless units), while the observables of class (ii) are de ned for both insulators and metals, and are single-valued. As for class (i), two observables are known: electrical polarization and the so-called axion" term in magnetoelectric response. For both observables the modulo 2 ambiguity is xed only after the termination of the insulating sample is speci ed. Furthermore in presence of some protecting symmetry only the values zero or (mod 2 ) are allowed: the observable becomes then a topological index. The most recent advances, and the most relevant open issues, concern the geometrical observables of class (ii), which notably include orbital magnetiza- tion and anomalous Hall conductivity (in both insulators and metals). Owing to their single-valuedness, the geometrical observables in class (ii) can also be de ned locally in coordinate space: they admit therefore a density". We have extended their de nitions to the cases of a noncrystalline and/or a macroscop- ically inhomogeneous sample, and even a bounded sample. We have pioneered this approach and we plan to investigate the issue further. The research is to be be conducted at the IOM (Istituto Officina dei Ma- terial), belonging to CNR (National Research Council), under the direction of Dr. Raffaele Resta. The PI will also hold a part-time appointment at the University of Trieste. Most of the Grant will support ongoing collaborations with some US research groups, including the cost of international travel (to the US) and extended stays of the PI, and possibly some coworkers, at selected US institutions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 19, 2020
- Source ID
- N000142012847
Entities
People
- Raffaele Resta
Organizations
- Consiglio Nazionale delle Ricerche
- Office of Naval Research
- United States Navy